In reality, 3D geometric data usually contains unwanted noise that obscures the features of the volumes of interest. Consequently, denoising is critical in the 3D geometric analysis; for example, in many imaging studies, smoothing methods are widely adopted in image processing tasks [1]}, [2]}. As shown in Figure REF , the objects (or regions) of interest are usually irregularly shaped. Many conventional denoising methods, such as Kernel smoothing [3]}, tensor product smoothing [4]}, thin plate spline smoothing [5]}, [6]}, and wavelet smoothing [7]}, suffer from the problem of “leakage" across the complex domains, which refers to the poor estimation over difficult regions caused by smoothing inappropriately across boundary features [8]}, [9]}, [10]}. Several techniques have been developed in the last decades to tackle the “leakage” problem when recovering the true signals. Many of the work focus on 2D manifold domains, such as the spline smoothing [9]}, [12]}, finite element analysis [13]}, and Kernel smoothing [14]}. For 3D cases, [15]} applied the discrete heat kernel smoothing to irregular image domains, and [16]} considered the finite element method for irregular 3D subjects.
